On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Objective Perfusion Assessment in Gracilis Muscle Interposition—A Novel Software-Based Approach to Indocyanine Green Derived Near-Infrared Fluorescence in Reconstructive Surgery

Background: Gracilis muscle interposition (GMI) is an established treatment option for complex perineal fistulas and reconstruction. The outcome is limited by complications such as necrosis, impaired wound healing and fistula persistence or recurrence. Quantifiable methods of assessing muscle flap perfusion intraoperatively are lacking. This study evaluates a novel and objective software-based assessment of indocyanine green near-infrared fluorescence (ICG-NIRF) in GMI. Methods: Intraoperative ICG-NIRF visualization data of five patients with inflammatory bowel disease (IBD) undergoing GMI for perineal fistula and reconstruction were analyzed retrospectively. A new software was utilized to generate perfusion curves for the specific regions of interest (ROIs) of each GMI by depicting the fluorescence intensity over time. Additionally, a pixel-to-pixel and perfusion zone analysis were performed. The findings were correlated with the clinical outcome. Results: Four patients underwent GMI without postoperative complications within 3 months. The novel perfusion indicators identified here (shape of the perfusion curve, maximum slope value, distribution and range) indicated adequate perfusion. In one patient, GMI failed. In this case, the perfusion indicators suggested impaired perfusion. Conclusions: We present a novel, software-based approach for ICG-NIRF perfusion assessment, identifying previously unknown objective indicators of muscle flap perfusion. Ready for intraoperative real-time use, this method has considerable potential to optimize GMI surgery in the future

The martyrdom effect : when pain and effort increase prosocial contributions

Most theories of motivation and behavior (and lay intuitions alike) consider pain and effort to be deterrents. In contrast to this widely held view, we provide evidence that the prospect of enduring pain and exerting effort for a prosocial cause can promote contributions to the cause. Specifically, we show that willingness to contribute to a charitable or collective cause increases when the contribution process is expected to be painful and effortful rather than easy and enjoyable. Across five experiments, we document this “martyrdom effect,” show that the observed patterns defy standard economic and psychological accounts, and identify a mediator and moderator of the effect. Experiment 1 showed that people are willing to donate more to charity when they anticipate having to suffer to raise money. Experiment 2 extended these findings to a non-charity laboratory context that involved real money and actual pain. Experiment 3 demonstrated that the martyrdom effect is not the result of an attribute substitution strategy (whereby people use the amount of pain and effort involved in fundraising to determine donation worthiness). Experiment 4 showed that perceptions of meaningfulness partially mediate the martyrdom effect. Finally, Experiment 5 demonstrated that the nature of the prosocial cause moderates the martyrdom effect: the effect is strongest for causes associated with human suffering. We propose that anticipated pain and effort lead people to ascribe greater meaning to their contributions and to the experience of contributing, thereby motivating higher prosocial contributions. We conclude by considering some implications of this puzzling phenomenon. Copyright © 2011 John Wiley & Sons, Ltd

Advances in multispectral and hyperspectral imaging for archaeology and art conservation

Multispectral imaging has been applied to the field of art conservation and art history since the early 1990s. It is attractive as a noninvasive imaging technique because it is fast and hence capable of imaging large areas of an object giving both spatial and spectral information. This paper gives an overview of the different instrumental designs, image processing techniques and various applications of multispectral and hyperspectral imaging to art conservation, art history and archaeology. Recent advances in the development of remote and versatile multispectral and hyperspectral imaging as well as techniques in pigment identification will be presented. Future prospects including combination of spectral imaging with other noninvasive imaging and analytical techniques will be discussed

Motor Preparatory Activity in Posterior Parietal Cortex is Modulated by Subjective Absolute Value

For optimal response selection, the consequences associated with behavioral success or failure must be appraised. To determine how monetary consequences influence the neural representations of motor preparation, human brain activity was scanned with fMRI while subjects performed a complex spatial visuomotor task. At the beginning of each trial, reward context cues indicated the potential gain and loss imposed for correct or incorrect trial completion. FMRI-activity in canonical reward structures reflected the expected value related to the context. In contrast, motor preparatory activity in posterior parietal and premotor cortex peaked in high “absolute value” (high gain or loss) conditions: being highest for large gains in subjects who believed they performed well while being highest for large losses in those who believed they performed poorly. These results suggest that the neural activity preceding goal-directed actions incorporates the absolute value of that action, predicated upon subjective, rather than objective, estimates of one's performance